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Update 2022-03-07 20:40

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Jean-Sébastien
2022-03-07 20:40:36 +01:00
parent 21bf9fdba5
commit 4808df71e6
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build/emdm_emwm_plm.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-02 Wed 15:45 -->
<!-- 2022-03-07 Mon 20:38 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1098,14 +1098,6 @@ Table of contents
<li>
<a href="./emdm_emwm_refl_oi.html#emdm_emwm_refl_oi">Oblique Incidence</a><span class="headline-id">emdm.emwm.refl.oi</span>
</li>
<li>
<a href="./emdm_emwm_refl_Fe.html#emdm_emwm_refl_Fe">Fresnel's Equations</a><span class="headline-id">emdm.emwm.refl.Fe</span>
</li>
<li>
<a href="./emdm_emwm_refl_Ba.html#emdm_emwm_refl_Ba">Brewster's Angle</a><span class="headline-id">emdm.emwm.refl.Ba</span>
</li>
</ul>
@@ -1624,13 +1616,13 @@ Table of contents
<p>
In matter regions without free charge and free current: Maxwell's equations are
</p>
\begin{align}
\begin{align*}
(i)~~ &amp;{\boldsymbol \nabla} \cdot {\bf D} = 0, \nonumber \\
(ii)~~ &amp;{\boldsymbol \nabla} \cdot {\bf B} = 0, \nonumber \\
(iii)~~ &amp;{\boldsymbol \nabla} \times {\bf E} = -\frac{\partial {\bf B}}{\partial t}, \nonumber \\
(iv)~~ &amp;{\boldsymbol \nabla} \times {\bf H} = \frac{\partial {\bf D}}{\partial t}.
\label{Gr(9.65)}
\end{align}
\end{align*}
<p>
For linear medium:
\[
@@ -1640,13 +1632,31 @@ For linear medium:
\]
If the medium is homogeneous (no spatial dependence of \(\varepsilon\) or \(\mu\)),
</p>
<div class="main div" id="orga20c833">
<div class="eqlabel" id="org28a8d44">
<p>
<a id="Max_lh"></a><a href="./emdm_emwm_plm.html#Max_lh"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org79eef6d">
<ul class="org-ul">
<li>Gr (9.65)</li>
</ul>
</div>
</div>
\begin{align}
(i)~~ &amp;{\boldsymbol \nabla} \cdot {\bf E} = 0, \nonumber \\
(ii)~~ &amp;{\boldsymbol \nabla} \cdot {\bf B} = 0, \nonumber \\
(iii)~~ &amp;{\boldsymbol \nabla} \times {\bf E} = -\frac{\partial {\bf B}}{\partial t}, \nonumber \\
(iv)~~ &amp;{\boldsymbol \nabla} \times {\bf B} = \mu \varepsilon \frac{\partial {\bf E}}{\partial t}.
\label{Gr(9.65)}
\tag{Max_lh}\label{Max_lh}
\end{align}
</div>
<p>
These are the same equations as in vacuum, except for the substitution of \(\mu_0 \varepsilon_0\) by \(\mu \varepsilon\).
</p>
@@ -1659,13 +1669,30 @@ v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}
\]
where the index of refraction of the material is defined as
</p>
<div class="main div" id="orgd0bce92">
<div class="main div" id="orga25a79e">
<p>
<b>Index of refraction</b>
</p>
<div class="eqlabel" id="orgc9df98d">
<p>
<a id="n"></a><a href="./emdm_emwm_plm.html#n"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org574afc6">
<ul class="org-ul">
<li>Gr (9.69)</li>
</ul>
</div>
</div>
<p>
{\bf Index of refraction}
\[
n \equiv \sqrt{\frac{\mu \varepsilon}{\mu_0 \varepsilon_0}}
\label{Gr(9.69)}
\]
n \equiv \sqrt{\frac{\mu \varepsilon}{\mu_0 \varepsilon_0}}
\tag{n}\label{n}
\]
</p>
</div>
@@ -1675,7 +1702,7 @@ Fact: for most materials, \(\mu\) is very close to \(\mu_0\), so
n \simeq \sqrt{\varepsilon_r}
\label{Gr(9.70)}
\]
with \(\varepsilon_r\) being the dielectric constant \ref{Gr(4.34)}.
with \(\varepsilon_r\) being the dielectric constant <a href="./emsm_esm_ld_sp.html#epsr">epsr</a>.
</p>
<p>
@@ -1716,7 +1743,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-03-02 Wed 15:45</p>
<p class="date">Created: 2022-03-07 Mon 20:38</p>
<p class="validation"></p>
</div>